Studies On Portfolio Selection Problems With Different Risk Measuresand Trading Constraints  Posted on:20141027  Degree:Doctor  Type:Dissertation  Country:China  Candidate:X T Cui  Full Text:PDF  GTID:1109330434971269  Subject:Operational Research and Cybernetics  Abstract/Summary:  PDF Full Text Request  As an important part of modern finance theory, investment science focuses on how to help investors make reasonable investment decisions and manage risk under the riskreturn framework. In1952, Markowitz proposed the famous meanvariance portfolio selection model, which has been regarded as the foundation of modern investment science. Over the past six decades, many researchers have made great efforts to extend meanvariance model. Different risk measures have been proposed from different perspectives. The advances and development of modern investment science provide efficient tools for risk management and theoretical guide for new financial innovations.Markowitz’s meanvariance model, however, has some evident drawbacks. The variance measures the overall risk of portfolio, while neglecting the marginal contributions of individual assets or factors. In practice, classical meanvariance model is merely used as a theoretical model, and it does not take into account of the practical features, such as cardinality constraint and minimum buyin threshold. Meanwhile, for the portfolios with asymmetry returns, mean and variance cannot grasp all the characteristics of portfolio returns. All of these drawbacks undermine the practical applications of meanvariance model.We focus in this thesis on the portfolio selection problems based on different risk measures and trading constraints in order to narrow the gap between investment theory and financial practice. The main contributions of the thesis are described as follows.The adoption of an appropriate factor model enables us to pin point the hidden forces that drive the movement of the market and contribution to the systematic risk of the market. We introduce the concept of factor risk to measure individual factor’s contribution to the overall risk, and construct the portfolio selection model with factor risk control. The resulting model can be reduced to an quadratically constrained quadratic program. By exploiting the special features of the model structure, we propose a special branchandbound algorithm which employs the secondorder cone relaxations as its bounding procedure. Numerical test indicates that our algorithm can optimize the model efficiently. Historical data from Hong Kong stock market are employed to analyze the empirical performance. Analysis results show that the portfolio selection model with factor risk control can help to generate robust portfolio and circumvent the influence of unpromising factors.The efficiency of portfolio selection models depends on the accuracy of model parameters. Since estimation error cannot be avoided in parameter estimation, we analyze the portfolio’s sensitivity to parameters, and construct portfolio selection model with parameter sensitivity constraint in an effort to reduce the negative influence of parameter estimation error to optimal portfolio. The resulting model is a nonconvex quadratically constrained quadratic program (nonconvex QCQP), which is NPhard. By decomposing the nonconvex constraints, we propose an efficient branchandbound algorithm with QP relaxation as the bounding procedure. Numerical experiment indicates that our branchandbound algorithm is competitive with the commercial software BARON. To examine the model efficiency, we analyze the effect of the parameter robustness improvement and outofsample performance using backtesting strategy. The analysis results indicate that the portfolio model with parameter sensitivity control can construct efficient portfolio with good parameter robustness.Cardinality and minimum buyin threshold constraints are often encountered in practical portfolio selection models due to the managerial and transaction cost considerations. We construct convex relaxations for this class of optimization problems via a new Lagrangian decomposition scheme. We show that the dual problem can be reduced to a secondorder cone program problem which is tighter than the continuous relaxation of the standard mixed integer quadratically constrained quadratic (MIQCQP) reformulation. We then propose a new MIQCQP reformulation which is more efficient than the standard MIQCQP reformulation in terms of the tightness of the continuous relaxations. Computational results are reported to demonstrate the tightness of the SOCP relaxation and the effectiveness of the new MIQCQP reformulation. Since variance does not grasp all features of the risk of portfolios with asymmetry return, we introduce ValueatRisk (VaR) constraint as a downside risk measure into meanvariance framework. VaR constraint is equivalent to probabilistic constraint and can be reduced to a group of mixed01linear constraints under finite discrete distributions. We first derive secondorder cone programming (SOCP) relaxation and semidefinite programming (SDP) relaxation for the problem via a new Lagrangian decomposition scheme. We then give a mixed integer quadratic programming (MIQP) reformulation of the problem and show that the continuous relaxation of the MIQP is exactly the SOCP relaxation. Computational results demonstrate the tightness of the new convex relaxations and the effectiveness of the new MIQP reformulation. Numerical results also suggest that the VaR constraint brings great computational challenge when there are large number of scenarios.Existing research results indicate that VaR based on scenarios or samples is not robust, while the parametric VaR sometimes exhibits large estimation error if the assumed distribution has large deviation from true distribution. Nonparametric VaR, on the other hand, is a robust estimator not relying on the distribution assumption. We propose portfolio selection models by incorporating nonparametric VaR into portfolio selection. Since the resulting problem is nonconvex and hard to solve, we develop an alternative direction algorithm based on augmented Lagrangian method. To show the performance of the proposed model, we carry out empirical analysis on the statistic performance and portfolio behavior using American market data. The empirical results show that nonparametric VaR generally behaves robust and the corresponding portfolio selection model generates portfolio with good performance.It is wellknown that the skewed return distribution is a prominent feature in nonlinear portfolio selection problems which involve derivative assets with nonlinear payoff structures. VaR is particularly suitable as a risk measure in nonlinear portfolio selection. Unfortunately, the nonlinear portfolio selection formulation using VaR risk measure is in general a computationally intractable optimization problem. We investigate in this thesis nonlinear portfolio selection models using approximate parametric VaR. More specifically, we use firstorder and second order approximations of VaR for constructing portfolio selection models, and show that the portfolio selection models based on Deltaonly, DeltaGammanormal and worstcase DeltaGamma VaR approximations can be reformulated as secondorder cone programs, which are polynomially solvable using interiorpoint methods. Our simulation and empirical results suggest that the model using DeltaGammanormal VaR approximation performs the best in terms of balancing the tradeoff between the approximation accuracy and computational efficiency.The thesis is organized as follows. In Chapter1, we briefly introduce the research background of portfolio selection problems and summarize the main contributions of the thesis. In Chapter2, we give an overview of the basic theory and research results of portfolio selection. Portfolio selection problems with factor risk control is studied in Chapter3. In Chapter4, we discuss the parameter sensitivity and propose a portfolio selection problem with parameter sensitivity control. Portfolio selection problems with cardinality and minimum buyin threshold constraints are investigated in Chapter5, while meanvariance portfolio optimization model with VaR constraint is presented and analyzed in Chapter6. In Chapter7, the portfolio selection problem based on nonparametric VaR is studied. In Chapter8, we propose the nonlinear portfolio selection based on parametric VaR. We analyze the approximation accuracy of different parametric VaR and present empirical performance of different models. Finally, we summarize in Chapter9the results of the thesis and discuss some future research perspectives.  Keywords/Search Tags:  Meanvariance model, risk measures, factor models, cardinality constraint, ValueatRisk, global optimization, mixedinteger quadratic programs, empirical study  PDF Full Text Request  Related items 
 
